Holding a license is like holding a driver's license; an appointment is like the car keys an insurer hands you. Without keys you still have the license, but you cannot drive for that insurer.
Appointment (Ins. Code §§1704, 1705): an insurer appoints a licensee by filing a notice of appointment, and the licensee must consent. Under §1704(a), the authority given by the appointment is effective as of the date the notice of appointment is signed, and it applies to later transactions and to the insurer's liability for the appointee's acts. Filing is still required. Under §1705, an insurer that appoints an applicant for an original license is deemed to declare that the applicant is of good reputation and worthy of the license.
Inactive license and surrender (Ins. Code §§1704(b), 1708):
A permanent license becomes inactive, not canceled, when all appointments end and any broker's bond is canceled.
An inactive license may be reactivated before it expires by filing a new appointment.
An inactive license does not permit its holder to transact any insurance that requires a valid, active license. Servicing existing clients is transacting (§35), so it is not allowed.
A licensee may surrender a license for cancellation at any time by written notice to the commissioner.
Termination (Ins. Code §§1710, 1711, 1712): a natural person's license ends at death (§1710). A copartnership ceases to be eligible to hold a license when it dissolves (§1711), and that ends its right to transact (§1712). Section 1712 makes an exception: the business may continue as a different entity if a natural person is named to exercise the license powers, ownership and control do not substantially change, and an application and fees are filed within 30 days after the change.